Groupe de Physique Statistique

The fluctuation-dissipation relation is calculated for a class of stochastic models obeying a master equation with continuous time. It is shown that in general the linear response cannot be expressed via time-derivatives of the correlation function alone, but an additional function $\xi(t,t_w)$, which has been rarely discussed before is required. This function depends on the two times also relevant for the response and the correlation and vanishes under equilibrium conditions. $\xi(t,t_w)$ can be expressed in terms of the propagators and the transition rates of the master equation but it is not related to any physical observable in an obvious way. Instead, it is determined by inhomogeneities in the temporal evolution of the distribution function of the stochastic variable under consideration. $\xi(t,t_w)$ is considered for some examples of stochastic models, in particular for an extremely simple kinetic random energy model. Even in this case $\xi(t,t_w)$ does not vanish. However, it can be related to the 'aging part' of the two-time correlation function. This fact is of importance in the discussion of out-of-equlibrium extensions of the FDT.